JEE MAIN - Mathematics (2019 - 11th January Morning Slot - No. 1)
The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :
$$4\sqrt 5 $$
$${{\sqrt 5 } \over 2}$$
$$2\sqrt 5 $$
$${{\sqrt 5 } \over 4}$$
Explanation
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Equation of circle
(x $$-$$ 1) (x $$-$$ 0) + (y $$-$$ 0) (y $$-$$ $${1 \over 2}$$) = 0
$$ \Rightarrow $$ x2 + y2 $$-$$ x $$-$$ $${y \over 2}$$ = 0
Equation of tangent of region is 2x + y = 0
$$\ell $$1 + $$\ell $$2 = $${2 \over {\sqrt 5 }} + {1 \over {2\sqrt 5 }}$$
= $${{4 + 1} \over {2\sqrt 5 }} = {{\sqrt 5 } \over 2}$$
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